login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A117724 Triangle T(n,k) = coefficient [x^n] of x^2/(1-(k+1)*x^2-x^3) for row n, and columns k = 0..n, read by rows. 2
0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 4, 9, 16, 25, 36, 49, 2, 4, 6, 8, 10, 12, 14, 16, 2, 9, 28, 65, 126, 217, 344, 513, 730, 3, 12, 27, 48, 75, 108, 147, 192, 243, 300, 4, 22, 90, 268, 640, 1314, 2422, 4120, 6588, 10030, 14674 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,12
LINKS
Nathaniel Johnston, Rows n = 0..50, flattened
FORMULA
T(n,k) = coefficient [x^n] ( x^2/(1-(k+1)*x^2-x^3) ).
T(n, 0) = A000931(n+1).
T(n, 1) = A008346(n-2) = (-1)^(n-1)*A119282(n-1).
T(n, 2) = A052931(n-2).
EXAMPLE
The table starts:
0;
0, 0;
1, 1, 1;
0, 0, 0, 0;
1, 2, 3, 4, 5;
1, 1, 1, 1, 1, 1;
1, 4, 9, 16, 25, 36, 49;
2, 4, 6, 8, 10, 12, 14, 16;
2, 9, 28, 65, 126, 217, 344, 513, 730;
3, 12, 27, 48, 75, 108, 147, 192, 243, 300;
MAPLE
t:=taylor(x^2/(1-(k+1)*x^2-x^3), x, 15):
seq(seq(coeff(t, x, n), k=0..n), n=0..12); # Nathaniel Johnston, Apr 27 2011
MATHEMATICA
T[n_, k_]:= T[n, k]= Coefficient[Series[x^2/(1-(k+1)*x^2-x^3), {x, 0, n+ 2}], x, n];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Magma)
m:=12;
R<x>:=PowerSeriesRing(Integers(), m+2);
A117724:= func< n, k | Coefficient(R!( x^2/(1-(k+1)*x^2-x^3) ), n) >;
[A117724(n, k): k in [0..n], n in [0..m]]; // G. C. Greubel, Jul 23 2023
(SageMath)
def A117724(n, k):
P.<x> = PowerSeriesRing(QQ)
return P( x^2/(1-(k+1)*x^2-x^3) ).list()[n]
flatten([[A117724(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Jul 23 2023
CROSSREFS
Sequence in context: A256306 A030548 A346690 * A255826 A339256 A277544
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Apr 13 2006
EXTENSIONS
Sign in definition corrected, offset set to -1 by Assoc. Eds. of the OEIS, Jun 15 2010
Edited by G. C. Greubel, Jul 23 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 19 09:37 EDT 2024. Contains 373501 sequences. (Running on oeis4.)